Comparison of ultrafast electron and X-ray diffraction – A computational study

Ab initio calculation of inelastic scattering

“…The link between IXS and EELS suggests that the codes developed here could be useful for detailed analysis of ultrafast electron diffraction (UED) data, as long as the nuclear-scattering contribution is included in the elastic terms. 71 Future extensions of this work would be to include the effect of nuclear motion in the IXS signal, as we have recently done for elastic scattering, 37,38 and to consider Compton ionization by the inclusion of continuum states either via multichannel quantum defect formalism [72][73][74] or a Dyson orbital approach. 75 We also aim to examine in greater detail the mapping of the wavefunction in momentum space made possible by inelastic measurements.…”

Theory of ultrafast x-ray scattering by molecules in the gas phase

“…We also note that ultrafast electron diffraction is a closely related experimental technique, both in terms of observables 74,75 and the physical nature of the scattering process. 56,76 Unsurprisingly, for sufficiently coherent electron beams, directly analogous effects to the coherent mixed component described in the current paper appear.…”

Fundamental Limits on Spatial Resolution in Ultrafast X-ray Diffraction

“…Interestingly, the limited subset of 20 trajectories is sufficient to capture the evolution of the dynamics qualitatively. In part, this reflects that the diffraction signal is dominated by the comparatively simple dynamics of the C-C bond [75], which is well reproduced by the smaller subset of trajectories, but the observation is more general since we know from earlier studies that a small number of trajectories can do a good job of capturing the essence of a reaction path [79]. This observation is also commensurate with recent work on the ring-opening reaction of CHD, which found that the time-dependent diffraction pattern for the reaction could be reproduced accurately by a comparatively small number of trajectories representative of the dynamics [6].…”

“…Numerical values for the damping factors at q = 10 Å −1 are shown in Table 1. Invariably, the damping at q = 10 Å −1 is on the order of 0.7 or less (down to ≈0.4 for H, but then H-atoms contribute little to the scattering signal [75]). A factor of 0.7 corresponds to 30% of the signal irrevocably lost due to the delocalized nature of the target.…”

“…Equation (12), when rotationally averaged, becomes the standard IAM formula shown in Equation (15). It is perhaps worthwhile to point out that elastic electron scattering results in an expression almost identical to Equation (12), with the main difference being that the form factors for electron scattering must account for the additional scattering from the nuclei [2,74,75].…”